Feedback control optimization of counter-flow simultaneous heat and mass exchange

ABSTRACT

A counter-flow simultaneous heat and mass exchange device is operated by directing flows of two fluids into a heat and mass exchange device at initial mass flow rates where ideal changes in total enthalpy rates of the two fluids are unequal. At least one of the following state variables in the fluids is measured: temperature, pressure and concentration, which together define the thermodynamic state of the two fluid streams at the points of entry to and exit from the device. The flow rates of the fluids at the points of entry and/or exit to/from the device are measured; and the mass flow rate of at least one of the two fluids is changed such that the ideal change in total enthalpy rates of the two fluids through the device are brought closer to being equal.

RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No.61/917,847, filed Dec. 18, 2013, the entire content of which isincorporated herein by reference.

BACKGROUND

In this century, the shortage of fresh water will surpass the shortageof energy as a global concern for humanity; and these two challenges areinexorably linked, as explained, for example, in the “Special Report onWater” in the 20 May 2010 issue of The Economist. Fresh water is one ofthe most fundamental needs of humans and other organisms; each humanneeds to consume a minimum of about two liters per day. The world alsofaces greater freshwater demands from farming and industrial processes.

The hazards posed by insufficient water supplies are particularly acute.A shortage of fresh water may lead to a variety of crises, includingfamine, disease, death, forced mass migration, cross-regionconflict/war, and collapsed ecosystems. Despite the criticality of theneed for fresh water and the profound consequences of shortages,supplies of fresh water are particularly constrained. 97.5% of the wateron Earth is salty, and about 70% of the remainder is locked up as ice(mostly in ice caps and glaciers), leaving only a fraction of all wateron Earth as available fresh (non-saline) water.

Moreover, the earth's water that is fresh and available is not evenlydistributed. For example, heavily populated countries, such as India andChina, have many regions that are subject to scarce supplies. Furtherstill, the supply of fresh water is often seasonally inconsistent.Meanwhile, demands for fresh water are tightening across the globe.Reservoirs are drying up; aquifers are falling; rivers are dying; andglaciers and ice caps are retracting. Rising populations increasedemand, as do shifts in farming and increased industrialization. Climatechange poses even more threats in many regions. Consequently, the numberof people facing water shortages is increasing. Naturally occurringfresh water, however, is typically confined to regional drainage basins;and transport of water is expensive and energy-intensive.

Additionally, water can be advantageously extracted from contaminatedwaste streams (e.g., from oil and gas production) both to produce freshwater and to concentrate and reduce the volume of the waste streams,thereby reducing pollution and contamination and reducing costs.

Nevertheless, many of the existing processes for producing fresh waterfrom seawater (or from brackish water or contaminated waste streams)require massive amounts of energy. Reverse osmosis (RO) is currently theleading desalination technology. In large-scale plants, the specificelectricity required can be as low as 4 kWh/m³ at 30% recovery, comparedto the theoretical minimum of around 1 kWh/m³; smaller-scale RO systems(e.g., aboard ships) are less efficient.

Other existing seawater desalination systems includethermal-energy-based multi-stage flash (MSF) distillation, andmulti-effect distillation (MED), both of which are energy- andcapital-intensive processes. In MSF and MED systems, however, themaximum brine temperature and the maximum temperature of the heat inputare limited in order to avoid calcium sulfate, magnesium hydroxide andcalcium carbonate precipitation, which leads to the formation of softand hard scale on the heat transfer equipment.

Humidification-dehumidification (HDH) desalination systems include ahumidifier and a condenser as their main components and use a carriergas (e.g., air) to desalinate brine streams. A simple version of thistechnology includes a humidifier, a condenser, and a heater to heat thebrine stream. In the humidifier, hot brine comes in direct contact withdry air, and this air becomes heated and humidified. In the condenser,the heated and humidified air is brought into (indirect) contact with acoolant (for example, cold brine) and gets dehumidified, producing purewater and dehumidified air. The HDH process operates at lower top brinetemperatures than MSF and MED systems, precipitation of scalingcomponents is hence avoided to some extent.

Another approach, described in U.S. Pat. No. 8,119,007 B2 (A. Bajpayee,et aL), uses directional solvent that directionally dissolves water butdoes not dissolve salt. The directional solvent is heated to dissolvewater from a salt solution into the directional solvent. The remaininghighly concentrated salt water is removed, and the solution ofdirectional solvent and water is cooled to precipitate substantiallypure water out of the solution.

The present inventor was also named as one of the inventors on thefollowing patent applications that include additional discussion of HDHand other processes for purifying water: U.S. application Ser. No.12/554,726, filed 4 Sep. 2009; U.S. application Ser. No. 12/573,221,filed 5 Oct. 2009; U.S. application Ser. No. 13/028,170, filed 15 Feb.2011; and U.S. application Ser. No. 13/241,907, filed 23 Sep. 2011; U.S.application Ser. No. 13/550,094, filed 16 Jul. 2012; U.S. applicationSer. No. 13/916,038, filed 12 Jun. 2013; and U.S. application Ser. No.13/958,968, filed 5 Aug. 2013.

SUMMARY

Apparatus and methods for counter-flow simultaneous heat and massexchange are described herein. Various embodiments of the apparatus andmethods may include some or all of the elements, features and stepsdescribed below.

In an embodiment of the method, a counter-flow simultaneous heat andmass exchange device is operated by directing flows of two fluids into aheat and mass exchange device at initial mass flow rates where idealchanges in total enthalpy rates of the two fluids are unequal. At leastone of the following state variables in the fluids is measured by one ormore sensors: temperature, pressure and concentration, which togetherdefine the thermodynamic state of the two fluid streams at the points ofentry to and exit from the device. The flow rates of the fluids at thepoints of entry and/or exit to/from the device are measured; and themass flow rate of at least one of the two fluids is changed such thatthe ideal change in total enthalpy rates of the two fluids through thedevice are brought closer to being equal.

The methods and apparatus allow operation of a heat and mass exchangedevice so that it always operates optimally or near optimally from theperspective of thermodynamic efficiency by controlling flows of thefluids by controlling flow controllers, such as pumps, blowers andvalves in the system. These methods and apparatus can be used, e.g., forheat and mass exchange in a humidification-dehumidification process forproducing fresh water from an aqueous source composition that includesdissolved species.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a counter-flow heat exchanger.

FIG. 2 illustrates the flow, temperature, and concentration indicatortransmitters in the heat exchanger of FIG. 1.

FIG. 3 is a flow chart illustrating the steps in a method operating thesystem.

FIG. 4 is a schematic illustration of a counter-flow cooling tower.

FIG. 5 is a schematic illustration of a counter-flow condenser.

FIG. 6a is a schematic illustration of a humidification-dehumidification(HDH) system with the various positions labeled where system parametersare measured and with flow dynamics illustrated.

FIG. 6b is a schematic illustration of a condenser from the HDH systemof FIG. 6b , wherein the condenser includes two stages, with each stageincluding three trays.

FIG. 7 is a flow chart for an HDH method FIG. 6a without intermediateextraction.

FIG. 8 is a flow chart for an HDH method with a single intermediateextraction.

FIGS. 9 and 10 provide a flow chart for a two-stage HDH method using theapparatus of FIG. 6a with a single intermediate extraction

FIG. 11 is a plot of the gained output ratio (GOR) as a function of themass flow ratio at different water temperatures for an example of themethod.

FIG. 12 is a plot of the non-dimensional rate of entropy generation as afunction of the heat capacity ratio for an example of the method.

In the accompanying drawings, like reference characters refer to thesame or similar parts throughout the different views; and apostrophesare used to differentiate multiple instances of the same or similaritems sharing the same reference numeral. The drawings are notnecessarily to scale, emphasis instead being placed upon illustratingparticular principles, discussed below.

DETAILED DESCRIPTION

The foregoing and other features and advantages of various aspects ofthe invention(s) will be apparent from the following, more-particulardescription of various concepts and specific embodiments within thebroader bounds of the invention(s). Various aspects of the subjectmatter introduced above and discussed in greater detail below may beimplemented in any of numerous ways, as the subject matter is notlimited to any particular manner of implementation. Examples of specificimplementations and applications are provided primarily for illustrativepurposes.

Unless otherwise defined, used or characterized herein, terms that areused herein (including technical and scientific terms) are to beinterpreted as having a meaning that is consistent with their acceptedmeaning in the context of the relevant art and are not to be interpretedin an idealized or overly formal sense unless expressly so definedherein. For example, if a particular composition is referenced, thecomposition may be substantially, though not perfectly pure, aspractical and imperfect realities may apply; e.g., the potentialpresence of at least trace impurities (e.g., at less than 1 or 2%) canbe understood as being within the scope of the description; likewise, ifa particular shape is referenced, the shape is intended to includeimperfect variations from ideal shapes, e.g., due to manufacturingtolerances. Percentages or concentrations expressed herein can representeither by weight or by volume. Processes, procedures and phenomenadescribed below can occur at ambient pressure (e.g., about 50-120kPa—for example, about 90-110 kPa) and temperature (e.g., −20 to 50°C.—for example, about 10-35° C.).

Although the terms, first, second, third, etc., may be used herein todescribe various elements, these elements are not to be limited by theseterms. These terms are simply used to distinguish one element fromanother. Thus, a first element, discussed below, could be termed asecond element without departing from the teachings of the exemplaryembodiments.

Spatially relative terms, such as “above,” “below,” “left,” “right,” “infront,” “behind,” and the like, may be used herein for ease ofdescription to describe the relationship of one element to anotherelement, as illustrated in the figures. It will be understood that thespatially relative terms, as well as the illustrated configurations, areintended to encompass different orientations of the apparatus in use oroperation in addition to the orientations described herein and depictedin the figures. For example, if the apparatus in the figures is turnedover, elements described as “below” or “beneath” other elements orfeatures would then be oriented “above” the other elements or features.Thus, the exemplary term, “above,” may encompass both an orientation ofabove and below. The apparatus may be otherwise oriented (e.g., rotated90 degrees or at other orientations) and the spatially relativedescriptors used herein interpreted accordingly.

Further still, in this disclosure, when an element is referred to asbeing “on,” “connected to,” “coupled to,” “in contact with,” etc.,another element, it may be directly on, connected to, coupled to, or incontact with the other element or intervening elements may be presentunless otherwise specified.

The terminology used herein is for the purpose of describing particularembodiments and is not intended to be limiting of exemplary embodiments.As used herein, singular forms, such as “a” and “an,” are intended toinclude the plural forms as well, unless the context indicatesotherwise. Additionally, the terms, “includes,” “including,” “comprises”and “comprising,” specify the presence of the stated elements or stepsbut do not preclude the presence or addition of one or more otherelements or steps.

Additionally, the various components identified herein can be providedin an assembled and finished form; or some or all of the components canbe packaged together and marketed as a kit with instructions (e.g., inwritten, video or audio form) for assembly and/or modification by acustomer to produce a finished product.

Dependent Versus Independent Heat and Mass Exchange Devices

Dependent heat and mass exchange devices are described herein.

An “independent” heat and mass exchange device has inlet states that donot depend on the operation of the device (e.g., choice of flow rates).In other words, an independent heat and mass exchange device has inletstates that depend only on external conditions.

A “dependent” heat and mass exchange device, in contrast, has inletstates that depend on the operation of the device (e.g., the choice offlow rates). This dependency usually exists because the outlets of theheat-and-mass-exchange (HME) apparatus serve as or are coupled with theinlets to other HME devices, and the outlets of the coupled HME devicescan serve as or be coupled with the inlets of the HME device inquestion. For example, in a humidification-dehumidification (HDH)system, the condenser and humidifier are dependent HME devices as, forexample, varying the flow rate of air in the condenser affects theoperation of the humidifier (as it is the same flow rate) and so affectsthe outputs at the outlets of the humidifier, in particular, at the airoutlet. The air leaving the humidifier enters the condenser; so theinput at the inlet to the condenser changes with a changing of the flowrate of air in the condenser.

When controlling an independent HME device, one need only determine thestates of the inputs and calculate the heat capacity ratio (HCR), andset the new mass flow rate ratio (MR) to MR_(new)=MR_(old)/HCR_(d).HCR_(d) is the modified heat capacity rate ratio and is further defined,below

There is no need for iteration, as changing the flow rate will notaffect the inlet states. In contrast, when controlling a dependent HMEdevice, the process is carried out iteratively, as changing the flowrate will change the inlet states, and so will affect the value ofHCR_(d).

Simplified Illustration of Heat-and-Mass-Exchange Optimization

In the illustration of FIG. 1, two fluids are passed in counter-flowthrough a heat and mass exchanger 10 such that there is heat and massexchange between the two fluids, wherein |Δ{dot over (H)}_(AB)|>0,|Δ{dot over (H)}_(CD)|>0, and |Δ{dot over (H)}_(AB)|≃|Δ{dot over(H)}_(CD)|, and wherein {dot over (m)}_(A)<{dot over (m)}_(B), and {dotover (m)}_(C)>{dot over (m)}_(D), where Δ{dot over (H)} is the energyloss/gained/transfer from a fluid from a first or second fluid source 12or 14 with the heat and mass exchanger 10, and where {dot over (m)} isthe mass flow rate. In one example, a first fluid from the first source12 is moist air being condensed/dehumidified, while a second fluid fromthe second source 14 is pure water being used to dehumidify the firstfluid.

In the illustration FIG. 2, a configuration of sensors including flowindicator transmitters (FIT) 16, temperature indicator transmitters(TIT) 18, and concentration indicator transmitters (CIT) 20 are mountedin fluid lines A and C upstream and in fluid lines B and D downstreamfrom the heat and mass exchanger 10 in the two fluid conduits.Equivalently, sensors/transmitters (e.g., temperature transmitter, flowtransmitter and concentrator transmitter) without indicators can also beused. The flow of the fluids through the conduits is governed (i.e.,increased or decreased) by respective flow control devices 22 in theinput conduits in response to the flow, temperature, and/orconcentration signals received from the sensors/transmitters 16, 18 and20. Optionally, pressure indicator transmitters or pressure transmittersmay also be included to measure pressure in the conduits; and thosereadings may be incorporated by the control system as a basis forcontrolling the flow of the fluid(s) with the flow control device(s) 22.

A flow chart of the control operation is shown in FIG. 3, starting withthe measurements 24 taken by the FIT 16, TIT 18, and CIT 20. Thesetransmitters communicate their measurement values via signals to anautomated controller, such as a programmable logic controller (PLC) 26,in which the equations for flow control are stored. Values calculated bythe PLC can optionally then be transmitted to a memory device (e.g., acomputer hard drive) 28 for nontransitory storage; and a signalincluding desired flow rates is transmitted to the flow controldevice(s) 22. The process is then repeatedly reiterated, re-commencingwith new measurements taken by the FIT 16, TIT 18, and CIT 20.

The target for the flow control is to achieve the following condition:Δ{dot over (H)}_(max,1)=Δ{dot over (H)}_(max,2), where Δ{dot over(H)}_(max,1) and Δ{dot over (H)}_(max,2) represent the maximum possiblechange in total enthalpy rates for the first and second fluids.Accordingly, for the heat and mass exchange device in FIGS. 1 and 2, thepreceding equation can be expanded as {dot over (m)}_(A)h_(A)−{dot over(m)}*_(B)h*_(B)={dot over (m)}*_(D)h*_(D)−{dot over (m)}_(C)h_(C), whereh_(A) is specific enthalpy evaluated at the actual state of the firstfluid from the first source 12, which can be defined by the parameters,temperature in line A (T_(A)), concentration in line A (C_(A)), andpressure in line A (P_(A)); h*_(B)is specific enthalpy evaluated at theideal state of the first fluid from the first source 12 at the exit ofthe device, which can be defined by the parameters, temperature in lineC (T_(C)), concentration at saturation (C_(sat)) and pressure in line B(P_(B)); h*_(D)is specific enthalpy evaluated at the ideal state offluid 2 (which can be defined by the parameters, T_(A) and P_(D)); h_(C)is specific enthalpy evaluated at the ideal state of fluid 2 (which canbe defined by the parameters, T_(C) and P_(C)); and {dot over (m)}* isthe ideal mass flow rate at the outlet.

Direct Contact Heat and Mass Exchangers

Next, we consider a counter-flow cooling tower serving as the heat andmass exchanger and as a control volume, CV (shown in FIG. 4), in which afirst fluid stream 34 is salt water and a second stream 36 is a mixtureof air and water vapor. Because all of the dry air that enters thedevice in the humid air stream 36 leaves in the humid air stream 36, themass flow rate of dry air is constant, as reflected in the followingequation:{dot over (m)} _(da) ={dot over (m)} _(da,i) ={dot over (m)}_(da,o),  (1)where m is mass; da is dry air; I is input; and o is output.

A mass balance on the water in the cooling tower 10 gives the mass flowrate of the water leaving the humidifier in the water stream 34 via thefollowing equation:{dot over (m)} _(w,o) ={dot over (m)} _(w,i) −{dot over (m)}_(da)(ω_(a,o)−ω_(a,i)),  (2)where w is the water; a is the air stream; and ω is the humidity ratio(i.e., kg of vapor per kg of dry air in the moist air mixture).

In order to determine the maximum possible change in enthalpy rate, wedetermine whether the air stream 36 or the water stream 34 is the hot(warmer) stream.

When the water 34 enters hotter than the air 36, the ideal conditionthat the water stream 34 can attain is that the temperature at the exitof the water stream equals the wet-bulb temperature of the air stream 36at the air-stream inlet 37. This equivalence corresponds to the enthalpydriving force, which is just the enthalpy potential difference betweenthe two streams 34 and 36 driving the heat and mass transfer, becomingzero at the exit 33 of the water stream 34. The ideal condition that themoist air stream can reach is saturation at the inlet temperature of thewater stream 34 and is a limit imposed by the rate processes(T_(a,o)≦T_(w,i)). When the air stream 36 enters the condenser 10 hotterthan the water stream 34, the ideal conditions that can be attained bythe air stream 36 and the water stream 34 differ from those in the casewith hot water entering the heat and mass exchanger 10. These conditionsagain correspond to the driving enthalpy difference becoming zero forthe respective streams.

Based on the above discussion, the effectiveness definition of acounter-flow direct contact heat and mass exchange (HME) device with hotwater entering is written as follows. The denominator of the term on theright hand side represents the ideal change in total enthalpy rate.

-   Case I, Δ{dot over (H)}_(max,w)<Δ{dot over (H)}_(max,a):

$\begin{matrix}{ɛ = \frac{{{\overset{.}{m}}_{w,i}h_{w,i}} - {{\overset{.}{m}}_{w,o}h_{w,o}}}{{{\overset{.}{m}}_{w,i}h_{w,i}} - {{\overset{.}{m}}_{w,o}h_{w,o}^{ideal}}}} & (3)\end{matrix}$

-   Case II, Δ{dot over (H)}_(max,w)>Δ{dot over (H)}_(max,a):

$\begin{matrix}{ɛ = \frac{{\overset{.}{m}}_{d\; a}\left( {h_{a,o} - h_{a,i}} \right)}{{\overset{.}{m}}_{d\; a}\left( {h_{a,o}^{ideal} - h_{a,i}} \right)}} & (4)\end{matrix}$Note that the First Law for the cooling tower 10 gives:

$\begin{matrix}{{0 = {\underset{\Delta\;{\overset{.}{H}}_{a}}{\underset{︸}{{\overset{.}{m}}_{d\; a}\left( {h_{a,i} - h_{a,o}} \right)}} + \underset{\underset{\Delta\;{\overset{.}{H}}_{w}}{︸}}{{{\overset{.}{m}}_{w,i}h_{w,i}} - {{\overset{.}{m}}_{w,o}h_{w,o}}}}},} & (5)\end{matrix}$where Δ{dot over (H)}_(w) is the change in total enthalpy rate for thefeed water stream 34 and Δ{dot over (H)}_(a) is the change in totalenthalpy rate of the moist air stream 36. One can similarly derive theeffectiveness definition when at the inlet 37 where the hot air stream36 enters the cooling tower 10.Indirect Contact Heat and Mass Exchangers:

Now consider a counter-flow condenser serving as the heat and massexchanger 10 (as shown in FIG. 5) in which one fluid stream 34 is purewater and the other stream 36 is a mixture of air and water vapor. Theair-vapor-mixture stream 36 is transferring heat to the water stream 34.In this process, some of the water vapor in the mixture 36 condenses outand forms a separate condensate stream 38. Since all of the dry air inthe air stream 36 and all of the water in the other fluid stream 34 thatenters the condenser 10 also leaves the condenser 10, the mass flow rateof dry air and mass flow rate of the water is constant, as reflected bythe following equations:{dot over (m)} _(da) ={dot over (m)} _(da,i) ={dot over (m)} _(da,o),and  (6){dot over (m)} _(w,o) ={dot over (m)} _(w,i).  (7)

The mass flow rate of the condensed water 38 can be calculated using thefollowing simple mass balance:{dot over (m)} _(pw) ={dot over (m)} _(da)(ω_(a,i)−ω_(a,0)).  (8)

To calculate the maximum total enthalpy rate change possible, the inlettemperatures and mass flow rates are determined. As explained before,the ideal condition corresponds to the enthalpy driving force becomingzero at the exit of the water stream 34 or at the exit of the air stream36. The ideal condition that the air stream 36 can reach at the exit 39is saturation at the inlet temperature of water. The water can at bestreach the dry bulb temperature of the air at its inlet 37. Again, thiscorresponds to the enthalpy driving force reaching zero at the air inlet37.

Based on the above discussion, the effectiveness definition of acounter-flow indirect contact HME device 10 is as follows. Thedenominator of the term on the right-hand side represents the idealchange in enthalpy rate in the following equations:

-   Case I, Δ{dot over (H)}_(max,w)<Δ{dot over (H)}_(max,a):

$\begin{matrix}{{ɛ = \frac{h_{w,i} - h_{w,o}}{h_{w,i} - h_{w,o}^{ideal}}};} & (9)\end{matrix}$

-   Case II, Δ{dot over (H)}_(max,w)>Δ{dot over (H)}_(max,a):

$\begin{matrix}{ɛ = {\frac{{{\overset{.}{m}}_{d\; a}\left( {h_{a,o} - h_{a,i}} \right)} - {{\overset{.}{m}}_{pw}h_{pw}}}{{{\overset{.}{m}}_{d\; a}\left( {h_{a,o}^{ideal} - h_{a,i}} \right)} - {{\overset{.}{m}}_{pw}h_{pw}}}.}} & (10)\end{matrix}$Note that the First Law for the condenser can be expressed as follows:

$\begin{matrix}{{0 = {\underset{\underset{\Delta\;{\overset{.}{H}}_{a}}{︸}}{{{\overset{.}{m}}_{d\; a}\left( {h_{a,i} - h_{a,o}} \right)} + {{\overset{.}{m}}_{{pw},i}h_{{pw},i}} - {{\overset{.}{m}}_{{pw},o}h_{{pw},o}}} + \underset{\underset{\Delta\;{\overset{.}{H}}_{w}}{︸}}{{\overset{.}{m}}_{w}\left( {h_{w,i} - h_{w,o}} \right)}}},} & (11)\end{matrix}$where Δ{dot over (H)}_(w) is the change in total enthalpy rate for thefeed water stream 34, and Δ{dot over (H)}_(a) is the change in totalenthalpy rate of the moist air stream 36.Overview of HDH System

In the embodiment, as shown in FIG. 6a , an aqueous feed 50 in the formof fracking or produced water (from oil or gas production) is fed intoan intermediate brine holding tank 52, from where it is fed through apre-heating heat exchanger 54 and then through a second heat exchanger56 in which the aqueous feed 50 receives heat transferred from a boiler,before the heated aqueous feed is sprayed into a humidifier 68, asdescribed in US 2013/0015051 A1, where pure water is vaporized from theaqueous feed 50. The aqueous feed 50 is circulated through the devicevia passages through liquid conduits that join the components of thesystem. In other embodiments, the humidifier stages 58 and 60 can bebubble-column humidifiers, as described in U.S. application Ser. No.13/916,038.

Ambient air 62 is also pumped via a flow controller, such as a fan orpump, through the humidifier stages 58 and 60 and serves as a carriergas for the vaporized water in the humidifier stages 58 and 60. Thehumidified carrier gas is then passed through a carrier-gas conduit andfed through a two-stage bubble-column condenser 64 and 66, as describedin US 2013/0074694 A1, and cooled therein to precipitate the water. Inthe embodiment of FIG. 6b , each of the condenser stages 64 and 66includes a plurality of bubble-column trays 65 and 67. Trays 65/67 inthe same stage 64/66 are under the same flow rates of water and air (andare held at a common, fixed temperature), while the mass flow rate ofair (and temperature) changes as you move between stages 64 and 66. Anadditional intermediate stream of the humidified carrier gas isextracted from the humidifier 68 and injected at an intermediatelocation in the condenser 70 via an intermediate exchange conduit 72.The precipitated water 74 is circulated via a flow controller (e.g., apump) from the condenser 70, through the preheating heat exchanger 54(where heat from the precipitated water 74 is transferred to the aqueousfeed 50). Respective portions of the precipitated water 74 are then (a)fed to the boiler, (b) removed for delivery to the customer, and (c)recirculated to the bubble-column condenser 70.

Meanwhile, the brine 76 remaining in the humidifier 68 from the aqueousfeed 50 after water is evaporated therefrom is discharged from thehumidifier via a brine outlet and fed through a crystallizer, a sludgethickener, and a filter press to produce a salt product that is removedfrom the system and a brine discharge that is directed into the brineholding tank 52 (and recirculated).

The humidifier 68, in this embodiment, is a dual-column bubble-columnhumidifier, and the condenser 70 is a bubble-column dehumidifier. Thehumidified carrier gas 62 from the humidifier 68 is fed into thecondenser 70 at the lowest section of the condenser 70 (from the top ofthe humidifier 68) and at an intermediate exchange conduit 72 (from anintermediate position of the humidifier 68). Water is precipitated fromthe carrier gas 62 as it cools while rising through the stages 66 and 64of the bubble-column condenser 70 and collected for productive use orfor release. Meanwhile, the dehumidified carrier gas is released fromthe top of the condenser 70 after passing through stage 66.

Control Algorithm for HDH (Operation with One Mass Flow Rate Ratio):

With reference to FIG. 6a , in a system without extraction or injection,where the feed flow rate ({dot over (m)}_(B4)) and the fresh water flowrate ({dot over (m)}_(H2)) are specified, there is flexibility inchoosing the air flow rate ({dot over (m)}_(A1)={dot over (m)}_(A3)) inorder to get HCR_(d)=1 (or within a specified margin of error above orbelow 1, wherein the specified margin of error may match the potentialerror due to the accuracy of the sensor(s) used), and hence maximumenergy efficiency (subscripts for the various parameters in this sectionrepresent the various points in the flow paths, as labeled in FIG. 6a ,where the specified properties can be measured using installations ofthe various sensors/transmitters specified above). As shown in thegeneral flowchart of FIG. 7 for N=0 (with reference to the apparatus ofFIG. 6a ), where N is the number of extractions, the first step indetermining this flow rate is by measuring 82 the following parametersvia sensors located at the specified positions in order to fullydetermine the thermodynamic states of points W1 and A3:

-   -   Pressure at W1 (P_(W1));    -   Temperature at W1 (T_(W1));    -   Volumetric flow rate at W1 (F_(W1));    -   Temperature at A3 (T_(A3));    -   Volumetric flow rate at A3 (F_(A3));    -   Relative humidity at A3 (φ_(A3)); and    -   Pressure at A3 (P_(A3)).        These properties can be measured directly or indirectly.        Examples of indirect measurements include measuring mass, which        will determine volume, and measuring the humidity ratio, which        will dictate the relative humidity.

The following thermophysical properties of these two points areevaluated 84 in the next step:

-   -   ρ_(W1)=density of water at T_(W1), P_(H1);    -   ρ_(A3)=density of moist air at T_(A3), φ_(A3);    -   ω_(A3)=humidity ratio at T_(A3), φ_(A3);    -   ω_(A4,min)=humidity ratio at saturation, T_(W1);    -   h_(w,W2,max)=enthalpy of water at T_(A3), P_(W1);    -   h_(w,W1)=enthalpy of water at T_(W1), P_(W1);    -   h_(da,A3)=enthalpy of dry air at T_(A3), P_(A3);    -   h_(da,A4,min)=enthalpy of dry air at T_(W1), P_(A3);    -   h_(v,A3)=enthalpy of water vapor at T_(A3), P_(A3);    -   h_(v,A4,min)=enthalpy of water vapor at T_(W1), P_(A3); and    -   h_(fg,a3)=enthalpy of vaporization at T_(A3), P_(A3).

From these values, the mass flow rates, {dot over (m)}, were calculated86 as follows:

-   -   {dot over (m)}_(H1)=ρ_(H1)×F_(W1);    -   {dot over (m)}_(A3)=ρ_(A3)×F_(A3);    -   {dot over (m)}_(da,A3)={dot over (m)}_(A3)/(1+ω_(A3));

The modified heat capacity ratio, HCR_(d), in the bubble columndehumidifier is then calculated 88 according to the following equation:

${H\; C\; R_{d}} = {\frac{{\overset{.}{m}}_{W\; 1}}{{\overset{.}{m}}_{{da},{A\; 3}}} \times {\frac{\left( {h_{w,{W\; 2},\max} - h_{w,{W\; 1}}} \right)}{\begin{matrix}{\left( {h_{{da},{A\; 3}} - h_{{da},{A\; 4},\min}} \right) + {\omega_{{A\; 4},\min}\left( {h_{v,{A\; 3}} - h_{v,{A\; 4},\min}} \right)} +} \\{\left( {\omega_{A\; 3} - \omega_{{A\; 4},\min}} \right)h_{{fg},{A\; 3}}}\end{matrix}}.}}$

HCR_(d) is compared 89 with the value 1. If HCR_(d) is to be greaterthan 1, the flow rate of air is increased 90. If HCR_(d) is less than 1,the flow rate of air is decreased 92. After waiting 94 for the system toreach steady operation, the process is repeated with the measurements82. If HCR_(d) is very close to 1 (within error due to measurements),then this is the optimal operating point for these conditions; and,after waiting 96 for a sampling time specified by the user, the processis repeated with the measurements 82.

In this embodiment, system specifications are as follows

-   -   T_(A1)=25° C.;    -   T_(wb,A1)=25° C.;    -   T_(B6)=90° C.;    -   {dot over (m)}_(B4)=0.242 kg/s;    -   {dot over (m)}_(W2)=0.242 kg/s;    -   T_(B4)=30° C.;    -   humidifier height=3 m;    -   number of trays in condenser=6;    -   terminal temperature difference (TTD) in a first heat exchanger        (HX1)=3° C.; and    -   TTD in chiller 75=5° C.

Results in the system from sequence of iterations (steps) of the processare presented in the following table:

step 1 2 3 4 5 6 7 8 9 10 {dot over (m)}_(A) [kg/s] 0.02 0.04 0.07 0.050.05 0.05 0.05 0.05 0.05 0.05 HCR_(d) [—] 1.60 1.13 0.84 0.99 1.06 1.021.01 1.00 1.00 1.00 GOR [—] 1.47 1.82 1.79 1.90 1.88 1.90 1.91 1.91 1.901.91 RR [—] 0.06 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07Extra Detail on how to Increase or Decrease the Mass Flow Rate of DryAir:

As shown in the specific flowchart of FIG. 8, the same procedure as isrecited above is carried out through the calculation 88 of HCR_(d). Wethen modify the mass flow rate ratio, MR, in step 93, such that (a) thenew mass flow rate ratio, MR=(previous mass flow rate ratio,MR_(previous))/(calculated HCR_(d)), or (b) if the mass flow rate ofwater is constant, the new mass flow rate of dry air=(previous mass flowrate of dry air)×(calculated HCR_(d)). The system then waits for steadystate operation to be established in step 94.

Control Algorithm for Two-Stage HDH (with a Single Extraction):

The flowchart of FIGS. 9 and 10 outlines a process for a two-stagehumidification-dehumidification process with a single intermediateextraction between bubble-column stages in the humidifier (betweenstages 60 and 58) and the condenser (between stages 66 and 64), thoughthe process can also be carried out with multiple extractions betweenadditional stages in the humidifier 68 and condenser 70.

This exemplification is carried out with three trays in stage 66 andwith three trays in stage 64. The height for each humidifier stage 58/60is 1.5 meters.

First, the system is operated as a single stage (i.e., the extractedstream duct to intermediate conduit 72 is closed); and the algorithm,above, is used to find 98 the appropriate mass flow rate of air 62 suchthat HCR_(d)=1.

Next, the following measurements are taken 100 by sensors to determinethe thermodynamic states of points W20 and A3:

-   -   Pressure at W20 (P_(W20));    -   Temperature at W20 (T_(W20));    -   Volumetric flow rate at W20 (F_(W20));    -   Temperature at A3 (T_(A3));    -   Volumetric flow rate at A3 (F_(A3));    -   Relative humidity at A3 (φ_(A3)); and    -   Pressure at A3 (P_(A3)).

Next, the following thermophysical properties to determine thethermodynamic states of W20 and A3 are evaluated 102:

-   -   ρ_(W20)=density of water at T_(W20), P_(W20);    -   ρ_(A3)=density of moist air at T_(A3), φ_(A3);    -   ω_(A3)=humidity ratio at T_(A3), φ_(A3);    -   ω_(A7,min)=humidity ratio at saturation, T_(W20);    -   h_(w,W2,max)=enthalpy of water at T_(A3), P_(W20);    -   h_(w,W20)=enthalpy of water at T_(W20), P_(W20);    -   h_(da,A3)=enthalpy of dry air at T_(A3), P_(A3);    -   h_(da,A7,min)=enthalpy of dry air at T_(W20), P_(A3);    -   h_(v,A3)=enthalpy of water vapor at T_(A3), P_(A3);    -   h_(v,A7,min)=enthalpy of water vapor at T_(W20), P_(A3); and    -   h_(fg,a3)=enthalpy of vaporization at T_(A3), P_(A3).

From these values, the mass flow rates, {dot over (m)}, were calculated104 as follows:{dot over (m)} _(W20)=ρ_(W20) ×F _(W20);{dot over (m)} _(A3)=ρ_(A3) ×F _(A3); and{dot over (m)} _(da,A3) ={dot over (m)} _(A3)/(1+ω_(A3)).

The modified heat capacity ratio, HCR_(d,2), in the bubble columndehumidifier is then calculated 106 according to the following equation:

${H\; C\; R_{d,2}} = {\frac{{\overset{.}{m}}_{W\; 1}}{{\overset{.}{m}}_{{d\; a},{A\; 3}}} \times {\frac{\left( {h_{w,{W\; 2},\max} - h_{w,{W\; 1}}} \right)}{\begin{matrix}{\left( {h_{{d\; a},{A\; 3}} - h_{{d\; a},{A\; 4},\min}} \right) + {\omega_{{A\; 7},\min}\left( {h_{v,{A\; 3}} - h_{v,{A\; 7},\min}} \right)} +} \\{\left( {\omega_{A\; 3} - \omega_{{A\; 7},\min}} \right)h_{{fg},{A\; 3}}}\end{matrix}}.}}$

HCR_(d,2) is then compared 107 with the value, 1; and if HCR_(d,2) is 1(or within a margin of error of 1), the following additionalmeasurements are taken in step 112:

-   -   Pressure at W1 (P_(W1));    -   Temperature at W1 (T_(W1));    -   Volumetric flow rate at W1 (F_(W1));    -   Temperature at A8 (T_(A8));    -   Volumetric flow rate at A8 (F_(A8));    -   Relative humidity at A8 (φ_(A8)); and    -   Pressure at A8 (P_(A8)).

If HCR_(d,2)≠1, the mass flow rate ratio, MR, in the second (hot) stage64 is modified 108 before step 112 such that the new mass flow rateratio, MR₂=(previous mass flow rate ratio, MR_(2,previous))/(calculatedHCR_(d.2)).

Next, as shown in the flowchart of FIG. 10, which is a continuation ofthe flowchart of FIG. 9, the same procedure is performed on the coolerstage 66; i.e., the following properties are evaluated 114 to determinethe thermodynamic states of points A8 and W1:

-   -   ρ_(W1)=density of water at T_(W1), P_(W1);    -   ρ_(A8)=density of moist air at T_(A8), φ_(A8);    -   ω_(A8)=humidity ratio at T_(A8), φ_(A8);    -   ω_(A4,min)=humidity ratio at saturation, T_(W1);    -   h_(w,W20,max)=enthalpy of water at T_(A8), P_(W1);    -   h_(w,W1)=enthalpy of water at T_(W1), P_(W1);    -   h_(da,A8)=enthalpy of dry air at T_(A8), P_(A8);    -   h_(da,A4,min)=enthalpy of dry air at T_(W1), P_(A8);    -   h_(v,A8)=enthalpy of water vapor at T_(A8), P_(A8);    -   h_(v,A4,min)=enthalpy of water vapor at T_(W1), P_(A8); and    -   h_(fg,a8)=enthalpy of vaporization at T_(A8), P_(A8).

From these values, the mass flow rates, {dot over (m)}, were calculated116 as follows:{dot over (m)} _(W1)=ρ_(W1) ×F _(W1);{dot over (m)} _(A8)=ρ_(A8) ×F _(A8);{dot over (m)} _(da,A8) ={dot over (m)} _(A8)/(1+ω_(A8));

The modified heat capacity ratio, HCR_(d,1), in the bubble columndehumidifier is then calculated 118 according to the following equation:

${H\; C\; R_{d,1}} = {\frac{{\overset{.}{m}}_{W\; 1}}{{\overset{.}{m}}_{{d\; a},{A\; 3}}} \times {\frac{\left( {h_{w,{W\; 20},\max} - h_{w,{W\; 1}}} \right)}{\begin{matrix}{\left( {h_{{d\; a},{A\; 3}} - h_{{d\; a},{A\; 4},\min}} \right) + {\omega_{{A\; 7},\min}\left( {h_{v,{A\; 3}} - h_{v,{A\; 4},\min}} \right)} +} \\{\left( {\omega_{A\; 3} - \omega_{{A\; 4},\min}} \right)h_{{fg},{A\; 3}}}\end{matrix}}.}}$

HCR_(d,1) and HCR_(d,2) are compared 119 with the value 1; and ifHCR_(d,1)≠1, the mass flow rate ratio in the first (cooler) stage 66 ismodified 120 such that the new mass flow rate ratio, MR₁=(previous massflow rate ratio, MR_(1,previous))/(calculated HCR_(d,1)).

The process is repeated from the measurement 100 of properties of H20and A3 until HCR_(d,1)=HCR_(d,2)=1 (or as close as possible), or untilthe change in the gained output ratio (GOR) and recovery ratio (RR)between iterations becomes negligible.

Results in the system from sequence of iterations (steps) of the processare presented in the following table:

step 1 2 3 4 5 6 {dot over (m)}_(A1) [kg/s] 0.05 0.05 0.12 0.12 0.120.12 {dot over (m)}_(A3) [kg/s] 0.05 0.03 0.03 0.03 0.03 0.03 HCR_(d,1)[—] 1.41 2.42 0.96 0.96 0.99 0.99 HCR_(d,2) [—] 0.62 1.14 0.97 0.99 0.991.00 GOR [—] 1.93 1.77 2.24 2.24 2.24 2.24 RR [—] 0.07 0.07 0.08 0.080.08 0.08In the above table and elsewhere herein, [-] indicates a non-dimensionalnumber.

EXEMPLIFICATION

Process Optimization Equations for Humidification-Dehumidification (HDH)

The following equations can be used for process optimization in ahumidification-dehumidification cycle for producing fresh water and/orfor concentrating and removing contaminants from an aqueous compositionusing the apparatus of FIG. 6a (and referencing the flow streams shownin FIG. 6a in the subscripts of the variables).

The thermodynamic balancing of the preheater 54 (where C_(p,W2) is thespecific heat in the hot stage) can be expressed as follows:

$\begin{matrix}{{\overset{.}{m}}_{W\; 2} = {{\overset{.}{m}}_{B\; 5} \cdot c_{P,{B\; 4}} \cdot {{\frac{1}{c_{P,{W\; 2}}}\mspace{14mu}\left\lbrack {{kg}\text{/}s} \right\rbrack}.}}} & (12)\end{matrix}$

The non-dimensional number for the heat capacity ratio (HCR) for the hothumidifier stage 58 (where WB is the wet bulb temperature and where thehot stage 58 is referenced as H2) can be expressed as follows:

$\begin{matrix}{\frac{{\overset{.}{m}}_{{d\; a},{A\; 3}}\left( {h_{B\; 6} - h_{A\; 2}} \right)}{{{\overset{.}{m}}_{B\; 5} \cdot c_{P,{B\; 4}} \cdot T_{B\; 6}} - {{\overset{.}{m}}_{B\; 20}^{*} \cdot c_{P,{B\; 4}} \cdot {WB}_{A\; 2}}} = {H\; C\;{{R_{H\; 2}\mspace{14mu}\lbrack - \rbrack}.}}} & (13)\end{matrix}$The non-dimensional number for the cold humidifier stage 60, referencedas H1, can be expressed as follows:

$\begin{matrix}{\frac{{\overset{.}{m}}_{{d\; a},{A\; 1}}\left( {h_{B\; 20} - h_{A\; 1}} \right)}{{{\overset{.}{m}}_{B\; 20} \cdot c_{P,{B\; 4}} \cdot T_{B\; 20}} - {{\overset{.}{m}}_{B\; 3} \cdot c_{P,{B\; 4}} \cdot {WB}_{A\; 1}}} = {H\; C\;{{R_{H\; 1}\mspace{14mu}\lbrack - \rbrack}.}}} & (14)\end{matrix}$The non-dimensional numbers for the hot and cold stages 64 and 66 of thebubble column condenser 70 can be expressed as follows:

$\begin{matrix}{{{\frac{{\overset{.}{m}}_{W\; 1}\left( {h_{w}❘{{T_{AB} - h_{w}}❘T_{W\; 1}}} \right)}{{\overset{.}{m}}_{{d\; a},{A\; 1}}\left\lbrack {{\left( {h_{ma}{{T_{A\; 8} - h_{ma}}}T_{W\; 1}} \right) - \mspace{20mu}{\left( {\omega{{T_{A\; 8} - \omega}}T_{W\; 1}} \right)h_{w}}}❘T_{A\; 8}} \right\rbrack} = {H\; C\;{R_{D\; 1}\mspace{14mu}\lbrack - \rbrack}}};}\mspace{76mu}} & (15) \\{\;{and}} & \; \\{{\frac{{\overset{.}{m}}_{W\; 1}\left( {h_{w}{{T_{AB} - h_{w}}}T_{W\; 1}} \right)}{{\overset{.}{m}}_{{d\; a},{A\; 3}}\left\lbrack {{\left( {h_{ma}{{T_{A\; 3} - h_{ma}}}T_{W\; 20}} \right) - \mspace{20mu}{\left( {\omega{{T_{A\; 3} - \omega}}T_{W\; 20}} \right)h_{w}}}❘T_{A\; 3}} \right\rbrack} = {H\; C\;{R_{D\; 2}\mspace{14mu}\lbrack - \rbrack}}},} & (16)\end{matrix}$where D1 represents the first stage 66 of the condenser 70, and where D2represents the second stage 64 of the condenser 70.

The optimal system conditions for the cold stage 66 of bubble-columncondenser 70 can be expressed as follows:HCR_(D1)=1 [−] at steady state.  (17)

Finally, the optimal system conditions for the hot stage 64 of thebubble-column condenser 70 can be expressed as follows:HCR_(D2)=1 [−] at steady state.  (18)

FIG. 11 shows the results of a programmed simulation. GOR is a metricfor the energy cost of the water produced and is defined as (mass rateof water produced)/(power required to clean the water). The power inthis equation is expressed as a mass rate of steam consumed [(mass rateof steam)=(thermal energy consumed in the desalination process)/(latentheat of boiling for water)]. Consequently, a higher GOR results in moreefficient operation of the system.

Specifically, FIG. 11 is a graphical demonstration of the effects ofbalancing. Each line represents a different peak brine temperature. Thepeak in each line demonstrates that for every peak brine temperature,there exists an optimal mass flow ratio. Furthermore, each of these massflow ratios is unique for the peak brine temperature.

FIG. 12 is a result from a similar simulation and demonstrates thatentropy generation is minimized when HCR is equal to 1, regardless ofthe temperature of the inlet stream. This result is significant becausepast research in humidification-dehumidification had shown the existenceof optimal mass flow ratios but also indicated that each of theseoptimal ratios was unique to a set of temperature conditions. HCR is amore suitable metric than mass flow ratio for defining the balancedcondition of a heat and mass exchanger because the balanced HCR value isalways the same (i.e., 1).

Automated Control System

The systems and methods of this disclosure (including controlling theflows of the fluids through the system) can be implemented using acomputing system environment. Examples of well-known computing systemenvironments and components thereof that may be suitable for use withthe systems and methods include, but are not limited to various forms ofautomated controllers, such as microcontrollers, personal computers,server computers, hand-held or laptop devices, tablet devices,multiprocessor systems, microprocessor-based systems, set top boxes,programmable consumer electronics, network PCs, minicomputers, mainframecomputers, distributed computing environments that include any of theabove systems or devices, and the like. Typical computing systemenvironments and their operations and components are described in manyexisting patents (e.g., U.S. Pat. No. 7,191,467, owned by MicrosoftCorp.).

The methods may be carried out via non-transitory computer-executableinstructions, such as program modules. Generally, program modulesinclude routines, programs, objects, components, data structures, and soforth that perform particular tasks or implement particular types ofdata. The methods may also be practiced in distributed computingenvironments where tasks are performed by remote processing devices thatare linked through a communications network. In a distributed computingenvironment, program modules may be nontransitorally stored in bothlocal and remote computer storage media including memory storagedevices.

The systems and methods of this disclosure may utilize a computer (e.g.,in the form of a microcontroller) to carry out the processes describedherein. Components of the computer may include, but are not limited to,a computer processor, a computer storage medium serving as memory, andcoupling of components including the memory to the computer processor. Amicrocontroller is a small computer including a single integratedcircuit containing a processor core, non-transitory computer storagemedia (memory), and programmable input/output peripherals and can beused as an embedded system. The microcontroller memory can include bothpermanent (nonvolatile) read-only memory (ROM) storing pre-programmedsoftware in the form of a compact machine code as well as volatileread-write memory for temporary data storage. The microcontroller canalso include an analog-to-digital converter if the light detector towhich it is electronically coupled transmits its illumination data inanalog format as well as a programmable interval timer to control, e.g.,the duration of activation of the indicator LED's.

The various processes described in the descriptions of this disclosurecan be encoded as software instructions in memory and executed by aprocessor to carry out the processes.

In describing embodiments of the invention, specific terminology is usedfor the sake of clarity. For the purpose of description, specific termsare intended to at least include technical and functional equivalentsthat operate in a similar manner to accomplish a similar result.Additionally, in some instances where a particular embodiment of theinvention includes a plurality of system elements or method steps, thoseelements or steps may be replaced with a single element or step;likewise, a single element or step may be replaced with a plurality ofelements or steps that serve the same purpose. Further, where parametersfor various properties or other values are specified herein forembodiments of the invention, those parameters or values can be adjustedup or down by 1/100^(th), 1/50^(th), 1/20^(th), 1/10^(th), 1/5^(th),1/3^(rd), 1/2, 2/3^(rd), 3/4^(th), 4/5^(th), 9/10^(th), 19/20^(th),49/50^(th), 99/100^(th), etc. (or up by a factor of 1, 2, 3, 4, 5, 6, 8,10, 20, 50, 100, etc.), or by rounded-off approximations thereof, unlessotherwise specified. Moreover, while this invention has been shown anddescribed with references to particular embodiments thereof, thoseskilled in the art will understand that various substitutions andalterations in form and details may be made therein without departingfrom the scope of the invention. Further still, other aspects, functionsand advantages are also within the scope of the invention; and allembodiments of the invention need not necessarily achieve all of theadvantages or possess all of the characteristics described above.Additionally, steps, elements and features discussed herein inconnection with one embodiment can likewise be used in conjunction withother embodiments. The contents of references, including referencetexts, journal articles, patents, patent applications, etc., citedthroughout the text are hereby incorporated by reference in theirentirety; and appropriate components, steps, and characterizations fromthese references may or may not be included in embodiments of thisinvention. Still further, the components and steps identified in theBackground section are integral to this disclosure and can be used inconjunction with or substituted for components and steps describedelsewhere in the disclosure within the scope of the invention. In methodclaims, where stages are recited in a particular order—with or withoutsequenced prefacing characters added for ease of reference—the stagesare not to be interpreted as being temporally limited to the order inwhich they are recited unless otherwise specified or implied by theterms and phrasing.

What is claimed is:
 1. A method of operating a network of at least twocounter-flow simultaneous heat and mass exchange devices fluidicallycoupled with each other, the method comprising: flowing at least twofluid streams, comprising a feed liquid and a carrier gas, incounter-flow through the heat and mass exchange devices at initial massflow rates where ideal changes in total enthalpy rates of the two fluidsare unequal, wherein the heat and mass exchange devices comprise ahumidifier and a condenser, wherein at least one of the humidifier andthe condenser comprises a plurality of humidification or condensingstages through which the fluids pass, and wherein the humidification orcondensing stages comprise bubble columns through which at least one ofthe fluids is bubbled; measuring at least one of the following statevariables in the fluid streams: temperature, pressure and concentration,which together define the thermodynamic states of all of the fluidstreams at at least one of the following: (a) the points of entry to theheat and mass exchange devices and (b) the points of exit from the heatand mass exchange devices; measuring the flow rates of the fluids at atleast one of the following: (a) the points of entry to the heat and massexchange devices and (b) the points of exit from the heat and massexchange devices; changing the mass flow rate of at least one of thefluids such that the ideal change in total enthalpy rates of the twofluids through at least one of the at least two heat and mass exchangedevices are brought closer to being equal; vaporizing water from thefeed liquid in the humidifier; transporting the vaporized water with thecarrier gas to the condenser; condensing the vaporized water from thecarrier gas in the condenser; extracting at least one of the fluids (a)at an intermediate stage of the humidifier and injecting the extractedfluid into an intermediate stage of the condenser or (b) at anintermediate stage of the condenser and injecting the extracted fluidinto an intermediate stage of the humidifier, wherein the intermediatestage in at least one of the humidifier and condenser is positionedbetween humidification or condensing stages; measuring at least oneproperty selected from temperature, pressure and concentration of theextracted fluid as the extracted fluid is passed between the humidifierand condenser; and measuring the flow rate of the extracted fluid as theextracted fluid is passed between the humidifier and condenser.
 2. Themethod of claim 1, wherein the feed liquid is selected from at least oneof flow-back water and produced water from oil or gas extraction.
 3. Amethod of operating a network of at least two counter-flow simultaneousheat and mass exchange devices fluidically coupled with each other, themethod comprising: flowing at least two fluid streams, comprising a feedliquid and a carrier gas, in counter-flow through the heat and massexchange devices at initial mass flow rates where ideal changes in totalenthalpy rates of the two fluids are unequal, wherein the heat and massexchange devices comprise a humidifier and a condenser; measuring atleast one of the following state variables in the fluid streams:temperature, pressure and concentration, which together define thethermodynamic states of all of the fluid streams at at least one of thefollowing: (a) the points of entry to the heat and mass exchange devicesand (b) the points of exit from the heat and mass exchange devices;calculating a heat capacity ratio based on the measured state variableand the measured flow rates; measuring the flow rates of the fluids atat least one of the following: (a) the points of entry to the heat andmass exchange devices and (b) the points of exit from the heat and massexchange devices; changing the mass flow rate of at least one of thecarrier gas and the feed liquid as a function of the calculated heatcapacity ratio and such that the ideal change in total enthalpy rates ofthe two fluids through at least one of the at least two heat and massexchange devices are brought closer to being equal; vaporizing waterfrom the feed liquid in the humidifier; transporting the vaporized waterwith the carrier gas to the condenser; condensing the vaporized waterfrom the carrier gas in the condenser; extracting at least one of thefluids (a) at an intermediate stage of the humidifier and injecting theextracted fluid into an intermediate stage of the condenser or (b) at anintermediate stage of the condenser and injecting the extracted fluidinto an intermediate stage of the humidifier; measuring at least oneproperty selected from temperature, pressure and concentration of theextracted fluid as the extracted fluid is passed between the humidifierand condenser; and measuring the flow rate of the extracted fluid as theextracted fluid is passed between the humidifier and condenser.
 4. Themethod of claim 3, further comprising iteratively calculating the heatcapacity ratio and changing the flow rate of at least one of the feedliquid and the carrier gas if the heat capacity ratio is not within aspecified margin of error of 1.